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Title
Reduced basis methods for low frequency electromagnetic problems / Christopher Lackner
AuthorLackner, Christopher
CensorSchöberl, Joachim
PublishedWien, 2016
Description45 Blätter : Diagramme
Institutional NoteTechnische Universität Wien, Diplomarbeit, 2016
LanguageEnglish
Document typeThesis (Diplom)
Keywords (EN)reduced Basis Method / Maxwell equations
URNurn:nbn:at:at-ubtuw:1-7219 Persistent Identifier (URN)
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 The work is publicly available
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Abstract (English)

In this thesis we introduce a new way for adaptively selecting snapshots to con- struct a reduced basis (RB) subspace for the numerical solution of parabolic differential equations. Our main insterest is in low frequency electromagnetic equations where the displacement currents can be neglected. Constructing the RB subspace by solving shifted stationary problems is a natural and often used attempt, based on the work of Grimme [7]. In [9] the identity of shifts and eigen- values of the reduced system was derived as a necessary optimality condition. Because the optimal spaces are not nested, Druskin, Lieberman and Zaslavsky proposed the usage of a nested sequence of spaces with adaptivly chosen shifts fitted to the eigenvalues in [6]. Using a modified version of the Kolmogorov Smirnow test statistic we derive an algorithm with a better fitting of the shifts to the eigenvalues than in [6]. We present tests on a 2D heat equation example and a 3D electromagnetic one and observe an improved convergence rate with our method.

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